A theoretical study on three long-range interactions between two nanoparticles under the humid condition

At the micro/nanoscale under the humid condition, the competition among three long-range interactions of the electrostatic, cohesive, and capillary forces dominates the adhesive behavior between two nanoparticles. In this study, explicit solutions of the interfacial adhesive energy between two nanoparticles are obtained through continuum modeling by considering the three long-range interactions between them, where the Coulomb theorem, the Lennard-Jones potential, and the Young-Laplace equation are taken into consideration. The present theoretical results show that the interfacial adhesive forces strongly depend on the three interactions, where the cohesive force and capillary force play more important roles in the competition for a smaller distance h between two nanoparticles, while the electrostatic force dominates the interactions for a larger distance h. Checking against present molecular dynamics simulations shows that the present continuum solution has high accuracy. This study should be of great help for deeply understanding the aggregation and separation of nanoparticles under the humid condition.